Find the values of t at which the particles collide t = If two objects travel th

Question

Find the values of t at which the particles collide

t =

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions r1(t) = (t^2, 6t - 8, t^2) r2(t) = (11t - 18, t2, 10t - 16) for t greater than equal to 0. Find the values of tat which the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t=

Explanation / Answer

t=2

at any instance r1(t) = r2 (t)

so t2 = 11t-18

6t-8 = t2

t2 = 10t-16

solving three equation we get t=2 root common in three quadratic equations.so at t=2 they will collide

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